404 dynamic force and power

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1. Dynamic force and power Achyut Paudel 069/ bme /404

2. Forces that result when an object moves through a fluid, or when a fluid moves past an object . Dynamic forces arise due to the relative motion of an object in a fluid. There must be motion. The concept of dynamic forces can be explained with the help of Newton’s second law.

3. The study of forces resulting from the impact of fluid jets and when fluids are diverted round pipe bends involves the application of Newton’s second law in the form of F = m.a. The forces are determined by calculating the change of momentum of the flowing fluids.    In nature these forces manifest themselves in the form of wind forces, and the impact forces of the sea on the harbour walls.   The operation of hydro-kinetic machines such as turbines depends on forces developed through changing the momentum of flowing fluids. Newton’s Second Law can be stated as: The force acting on a body in a fixed direction is equal to rate of increase of momentum of the body in that direction. F= m.a = m.du /t = ρ . V.du /t = Q. ρ .du = Q. ρ .(v-u ) The force act in the direction of change in velocity dv.

4. Power due to fluid P= F.u = Q. ρ .(v-u).u

5. Water Skiing V i Water Particle V f Two things happen to the particle of water when it comes in contact with the ski. It’s direction will change It’s speed will be reduced This means the particle underwent acceleration, which means forces must have been acting on the particle.

6. The Force on the Water Particle V i V f V V = V f - V i F = ma Acceleration is change in velocity over time F = m ( V / t) The force must act in the same direction as the acceleration vector, and the acceleration vector must act in the same direction as the change in velocity vector determined above. F Newton's 2nd Law

7. The Force on the Ski (Dynamic Fluid Force) Newton’s 3 rd Law: for every force there is an equal and opposite force We’ve determined the force of the ski on the water, therefore we now know the force of the water on the ski. F This force can be broken down into components that act perpendicular and parallel to the direction of motion. Lift: Always perpendicular to motion. Not necessarily in the up direction. Drag : Always parallel to motion.

8. F  ½C D Av 2 C D = Drag coefficient  = Fluid density A = Surface area perpendicular to flow v = Relative velocity of object and fluid

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